A fully nonlinear method base on potential flow theory is proposed to simulate nonlinear interaction between incident waves and semi-submersible. In the boundary element method (BEM), auxiliary functions are introduced to calculate wave forces indirectly after the boundary integral equation is solved. The fully nonlinear boundary conditions are considered to track the free surface with total Lagrangian method, which has better numerical stability. A blocked structured mesh of free surface for the semi-submersible is constructed which facilitates the reconstruction and smoothing of the numerical grids with the least square method once the free surface is updated in time domain. The results of fully nonlinear numerical program are verified by convergence analysis and comparison with that of frequency domain, based on which, the hydrodynamic response of the semi-submersible under different incident waves are studied, and the strong nonlinear phenomena such as wave run-ups on the columns are also discussed.


With the development of ocean engineering to the deep sea, the semi-submersibles are more suitable for working in harsh marine environment compared with other offshore platforms. It is vital to study the nonlinear hydrodynamic behavior of semi-submersibles in waves at the design phase. Numerical schemes based on potential flow theory has better time efficient than CFD and provide results with sufficient precision in engineering. Different strong nonlinear phenomena may occur on the semi-submersible in deep sea (Swan, 1997), which cannot be predicted by linear or second-order diffraction theory accurately (Sweetman, 2002). The problems of higher-order potential flow method are too complex with little significance, while fully nonlinear potential flow method is rather easier and more immediate in produce higher-order results, which proves to be an ideal method for studying the nonlinear effect of waves interacting with floating body (Wang and Wu, 2010). Longuet-Higgins and Cokelet (1978) first proposed the fully nonlinear theory in time domain, which was applied in analyzing two-dimensional nonlinear problems, and this method was not better developed due to the limitations of computer performance, but in recent years, the fully nonlinear method has greatly improved in computing efficiency (Dombre and Harris, 2019) and gradually developed maturely. The application of fully nonlinear method is carried out in the numerical tank (Chen, 1994) or in an open water in general, the latter scheme is more popular and easier to be implemented. Zhou (2015) studied the hydrodynamic behavior of a truncated cylinder based on fully nonlinear theory, Kim (2021) proposed a fully nonlinear method and analyzed the nonlinear hydrodynamic performance of freely floating structures in nonlinear water waves. In addition to obtain each order wave forces, the strong nonlinear hydrodynamic phenomena can also be predicted by fully nonlinear method such as wave run-ups along the columns of the semi-submersible and fluid interference between the columns (Zhang, 2021). However, most of research about fully nonlinear method is limited to simple geometric objects interacting with waves, the application of this method in estimating the hydrodynamic performance of a semi-submersible is still insufficient.

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